Of 200 youthful gamers (under 18) who tried the new Z-Box-Plus game, 160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over). The 95 percent confidence interval for the difference of proportions would be approximately:
A)[+.013, +.263].
B)[-.014, +.188].
C)[-.003, +.163].
D)[+.057, +.261].

Question

Quizplus · Accepted Answer

To find the confidence interval for the difference of proportions, we can use the formula

(point estimate) ± (critical value) × (standard error)

where the point estimate is the difference between the sample proportions (160/200 - 144/200 = 0.08), the critical value is found using a standard normal distribution for a 95% confidence interval (z* = 1.96), and the standard error is given by

sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)

where p1 = proportion of excellent ratings among youths, p2 = proportion of excellent ratings among adults, n1 = sample size of youths, and n2 = sample size of adults.

Plugging in the values, we get a confidence interval of approximately [-0.003, 0.163], which is closest to choice C.

Of 200 Youthful Gamers (Under 18) Who Tried the New